Nonlinear identification

Modeling and identification of mechanical systems constitute an essential stage in practical control design and applications. Controllers commanding systems that operate at varying conditions or require high precision operation raise the need for a nonlinear approach in modeling and identification. Most mechanical systems used in industry are composed of masses moving under the action of position and velocity dependent forces. These forces exhibit nonlinear behavior in certain regions of operation. For a multi-mass rotational system, the nonlinearities, like Coulomb friction and dead zone, significantly influence the system operation when the rotation changes direction. The paper presents nonlinear modeling and identification of a DC motor rotating in two directions together with real time experiments. Linear and nonlinear models for the system are obtained for identification purposes, and the major nonlinearities in the system, such as Coulomb friction and dead zone, are investigated and integrated in the nonlinear model. The Hammerstein nonlinear system approach is used for identification of the nonlinear system model. Online identification of the linear and nonlinear system models is performed using the recursive least squares method. Results of the real time experiments are graphically and numerically presented, and the advantages of the nonlinear identification approach are revealed.

In this paper the adaptive nonlinear identification and trajectory tracking are discussed via dynamic neural networks. By means of a Lyapunov-like analysis we determine stability conditions for the identification error. Then we analyze the trajectory tracking error by a local optimal controller. An algebraic Riccati equation and a differential one are used for the identification and the tracking error analysis. As our main original contributions, we establish two theorems: the first one gives a bound for the identification error and the second one establishes a bound for the tracking error. We illustrate the effectiveness of these results by two examples: the second-order relay system with multiple isolated equilibrium points and the chaotic system given by Duffing equation.

B-Spline Neural Network (BSNN), a type of basis function neural network, is trained by gradient-based methods which may fall into local minima during the learning procedure. To overcome the limitations encountered by gradient-based optimization methods, we propose differential evolution (DE) -an evolutionary computation methodology -which can provide a stochastic search to adjust the control points of a BSNN. In this paper, we propose six DE approaches using chaotic sequences based on logistic mapping to train a BSNN. Chaos describes the complex behavior of a nonlinear deterministic system. The application of chaotic sequences instead of random sequences in DE is a powerful strategy to diversify the DE population and improve the DE's performance in preventing premature convergence to local minima. The numerical results presented here indicate that chaotic DE was effective for building a good BSNN model for the nonlinear identification of an experimental nonlinear yo-yo motion control system. # 2007 Published by Elsevier B.V.

Most processes in industry are characterized by nonlinear and time-varying behavior. Nonlinear system identification is becoming an important tool which can be used to improve control performance and achieve robust fault-tolerant behavior. Among the different nonlinear identification techniques, methods based on neuro-fuzzy models are gradually becoming established not only in the academia but also in industrial applications. Neuro-fuzzy modeling can be regarded as a gray-box technique on the boundary between neural networks and qualitative fuzzy models. The tools for building neuro-fuzzy models are based on combinations of algorithms from the fields of neural networks, pattern recognition and regression analysis. In this paper, an overview of neuro-fuzzy modeling methods for nonlinear system identification is given, with an emphasis on the tradeoff between accuracy and interpretability.

An important problem in engineering is the identification of nonlinear systems, among them radial basis function neural networks (RBF-NN) using Gaussian activation functions models, which have received particular attention due to their potential to approximate nonlinear behavior. Several design methods have been proposed for choosing the centers and spread of Gaussian functions and training the RBF-NN. The selection of RBF-NN parameters such as centers, spreads, and weights can be understood as a system identification problem. This paper presents a hybrid training approach based on clustering methods (k-means and c-means) to tune the centers of Gaussian functions used in the hidden layer of RBF-NNs. This design also uses particle swarm optimization (PSO) for centers (local clustering search method) and spread tuning, and the Penrose–Moore pseudoinverse for the adjustment of RBF-NN weight outputs. Simulations involving this RBF-NN design to identify Lorenz’s chaotic system indicate that the performance of the proposed method is superior to that of the conventional RBF-NN trained for k-means and the Penrose–Moore pseudoinverse for multi-step ahead forecasting.

This paper presents an adaptive neuro-fuzzy inference system (ANFIS) for USD/JPY exchange rates forecasting. Previous work often used time series techniques and neural networks (NN). ANFIS can be used to better explain solutions to users than completely black-box models, such as NN. The proposed neurofuzzy rule based system applies some technical and fundamental indexes as input variables. In order to generate membership functions (MFs), we make use of fuzzy clustering of the output space. The neuro-fuzzy model is tested with 28 candidate input variables for both currencies. For the purpose of comparison, Sugeno-Yasukawa model, feedforward multi-layer neural network, and multiple regression are benchmarked. The comparison demonstrates that the presented algorithm shows its superiority in terms of prediction error minimization, robustness and flexibility.

In this paper describing functions inversion is used and the restoring force of a nonlinear element in a MDOF system is characterized. The describing functions can be obtained using linearized frequency response functions (FRFs). The response of the system to harmonic excitation forces at distinct frequencies close to the resonant frequency results in linearized FRFs. The nonlinear system can be approximated at each excitation frequency by an equivalent linear system. This approximation leads to calculation of the first-order describing functions. By having the experimental describing functions calculated and the system's responses corresponding to the nonlinear element (measured or interpolated), nonlinear parameter identification can be performed. Two numerical and experimental case studies are provided to show the applicability of this method.

The new approach for identification of synchronous generator using Hammerstein model and with piecewise linear map is investigated in this paper. In this method, synchronous generator model consists of a linear-dynamic block and a nonlinear-static block. The identification method simultaneously approximates these blocks without requiring prior assumptions on the form of the static non-linearity. In this study, the field voltage is considered as the input and the active output power and the terminal voltage are considered as the outputs of the synchronous generator. Experimental results show good accuracy of the identified model.

Preisach model is a well-known hysteresis identification method in which the hysteresis is modeled by linear combination of hysteresis operators. Although Preisach model describes the main features of system with hysteresis behavior, due to its rigorous numerical nature, it is not convenient to use in real-time control applications. Here a novel neural network approach based on the Preisach model is addressed, provides accurate hysteresis nonlinearity modeling in comparison with the classical Preisach model and can be used for many applications such as hysteresis nonlinearity control and identification in SMA and Piezo actuators and performance evaluation in some physical systems such as magnetic materials. To evaluate the proposed approach, an experimental apparatus consisting one-dimensional flexible aluminum beam actuated with an SMA wire is used. It is shown that the proposed ANN-based Preisach model can identify hysteresis nonlinearity more accurately than the classical one. It also has powerful ability to precisely predict the higher-order hysteresis minor loops behavior even though only the first-order reversal data are in use. It is also shown that to get the same precise results in the classical Preisach model, many more data should be used, and this directly increases the experimental cost.

This paper addresses the identification and control of nonlinear systems by means of Fuzzy Hammerstein (FH) models, which consist of a static fuzzy model connected in series with a linear dynamic model. For the identification of nonlinear dynamic systems with the proposed FH models, two methods are proposed. The first one is an alternating optimization algorithm that iteratively refines the estimate of the linear dynamics and the parameters of the static fuzzy model. The second method estimates the parameters of the nonlinear static model and of the linear dynamic model simultaneously by using a constrained recursive least-squares algorithm. The obtained FH model is incorporated in a model-based predictive control scheme and a new constraint-handling method is presented. A simulated water-heater process is used as an illustrative example. A comparison with an affine neural network and a linear model is given. Simulation results show that the proposed FH modeling approach is useful for modular parsimonious modeling and model-based control of nonlinear systems.

This paper presents the nonlinear identification of a capacitive dual-backplate microelectromechanical systems (MEMS) microphone. First, a nonlinear lumped element model of the coupled electromechanical microphone dynamics is developed. Nonlinear finite element analyses are performed to verify the accuracy of the lumped linear and cubic stiffnesses of the diaphragm. In order to experimentally extract the system parameters, an approximate solution using the secondorder multiple scales method is synthesized for a nonlinear microphone model, subject to an electrical step input. A nonlinear least-squares technique is then implemented to extract system parameters from laser vibrometry data of the diaphragm motion. The results indicate that the theoretical fundamental resonant frequency, damping ratio and nonlinear stiffness parameter agree with the corresponding extracted experimental parameters with 95% confidence interval estimates. r

his article deals with the identification of nonlinear models T in observer canonical form of hydraulic servo-drives from sampled data of input-output measurements. The data are processed by a modified Recursive Instrumental Variables algorithm, to provide input-output relationships of the plant dynamics. From the parameters of the input-output relations, continuous state-space nonlinear models can be derived. Tests were performed on a strongly nonlinear hydraulic drive which has been used for research in our laboratory for several years. Results demonstrate good correspondence between the data and the identified models.

B-spline neural network (BSNN), a type of basis function neural network, is trained by gradient-based methods, which may fall into local minimum during the learning procedure. To overcome the problems encountered by the conventional learning methods, differential evolution (DE)  an evolutionary computation methodology  can provide a stochastic search to adjust the control points of a BSNN are proposed. DE incorporates an efficient way of self-adapting mutation using small populations. The potentialities of DE are its simple structure, easy use, convergence property, quality of solution and robustness. In this paper, we propose a modified DE using chaotic sequence based on logistic map to train a BSNN. The numerical results presented here indicate that the chaotic DE is effective in building a good BSNN model for nonlinear identification of an experimental nonlinear yo-yo motion control system.

In this paper a model selection algorithm for a nonlinear system identification method is proposed to study functional magnetic resonance imaging (fMRI) effective connectivity. Unlike most other methods, this method does not need a pre-defined structure/model for effective connectivity analysis. Instead, it relies on selecting significant nonlinear or linear covariates for the differential equations to describe the mapping relationship between brain output (fMRI response) and input (experiment design). These covariates, as well as their coefficients, are estimated based on a least angle regression (LARS) method.

In this paper the adaptive nonlinear identification and trajectory tracking are discussed via dynamic neural networks. By means of a Lyapunov-like analysis we determine stability conditions for the identification error. Then we analyze the trajectory tracking error by a local optimal controller. An algebraic Riccati equation and a differential one are used for the identification and the tracking error analysis. As our main original contributions, we establish two theorems: the first one gives a bound for the identification error and the second one establishes a bound for the tracking error. We illustrate the effectiveness of these results by two examples: the second-order relay system with multiple isolated equilibrium points and the chaotic system given by Duffing equation.

Modeling and identification of mechanical systems constitute an essential stage in practical control design and applications. Controllers commanding systems that operate at varying conditions or require high precision operation raise the need for a nonlinear approach in modeling and identification. Most mechanical systems used in industry are composed of masses moving under the action of position and velocity dependent forces. These forces exhibit nonlinear behavior in certain regions of operation. For a multi-mass rotational system, the nonlinearities, like Coulomb friction and dead zone, significantly influence the system operation when the rotation changes direction. The paper presents nonlinear modeling and identification of a DC motor rotating in two directions together with real time experiments. Linear and nonlinear models for the system are obtained for identification purposes, and the major nonlinearities in the system, such as Coulomb friction and dead zone, are investigated and integrated in the nonlinear model. The Hammerstein nonlinear system approach is used for identification of the nonlinear system model. Online identification of the linear and nonlinear system models is performed using the recursive least squares method. Results of the real time experiments are graphically and numerically presented, and the advantages of the nonlinear identification approach are revealed.

This paper presents some preliminary results of an ongoing project. A pattern classification algorithm is being developed and embedded into a Field-Programmable Gate Array (FPGA) and microprocessor-based data processing core in this project. The goal is to enable and optimize the functionality of onboard data processing of nonlinear, nonstationary data for smart wireless sensing in structural health monitoring. Compared with traditional microprocessor-based systems, fast growing FPGA technology offers a more powerful, efficient, and flexible hardware platform including on-site (field-programmable) reconfiguration capability of hardware. An existing nonlinear identification algorithm is used as the baseline in this study. The implementation within a hardware-based system is presented in this paper, detailing the design requirements, validation, tradeoffs, optimization, and challenges in embedding this algorithm. An off-the-shelf high-level abstraction tool along with the Matlab/Simulink environment is utilized to program the FPGA, rather than coding the hardware description language (HDL) manually. The implementation is validated by comparing the simulation results with those from Matlab. In particular, the Hilbert Transform is embedded into the FPGA hardware and applied to the baseline algorithm as the centerpiece in processing nonlinear time histories and extracting instantaneous features of nonstationary dynamic data. The selection of proper numerical methods for the hardware execution of the selected identification algorithm and consideration of the fixed-point representation are elaborated. Other challenges include the issues of the timing in the hardware execution cycle of the design, resource consumption, approximation accuracy, and user flexibility of input data types limited by the simplicity of this preliminary design. Future work includes making an FPGA and microprocessor operate together to embed a further developed algorithm that yields better computational and power efficiency.

A new bounded-error approach for the identification of discrete time hybrid systems in the piece-wise affine (PWA) form is introduced. The PWA identification problem involves the estimation of the number of affine submodels, the parameters of affine submodels and the partition of the PWA map from data. By imposing a bound on the identification error, we formulate the PWA identification problem as a MIN PFS problem (partition into a minimum number of feasible subsystems) and propose a greedy clustering-based method for tackling it. The proposed approach yields to better results than the greedy randomized relaxation algorithm used in previous methods. Also, it is not sensitive to the overestimation of model orders and changes in the tuning parameters and therefore finding a right combination of the tuning parameters of the algorithm to get a model with prescribed bounded prediction error is simple

Constructing nonlinear structural dynamic models is a goal for numerous research and development organizations. Such a predictive capability is required in the development of advanced, high-performance aircraft structures. Specifically, the ability to predict the response of complex structures to engine induced and aero acoustic loading has long been a United States Air Force (USAF) goal. Sonic fatigue has plagued the USAF since the advent and adoption of the turbine engine. While the problem has historically been a maintenance one, predicting the dynamic response is crucial for future aerospace vehicles. Decades have been spent investigating the dynamic response and untimely failure of aircraft structures, yet little work has been accomplished towards developing practical nonlinear prediction methods. Further, the last decade has witnessed an appreciable amount of work in the area of nonlinear parameter identification. This paper outlines a unique and important extension of a recently introduced nonlinear identification method: Nonlinear Identification through Feedback of the Outputs (NIFO). The novel extension allows for a ready means of identifying nonlinear parameters in reduced order space using experimental data. The nonlinear parameters are then used in the assembly of reduced order models, thus providing researchers with a means of conducting predictive studies prior to expensive and questionable experimental efforts. This paper details both an analytical and experimental study conducted on a well-characterized clamped-clamped beam subjected to broadband random loading. Amplitude dependent, constant stiffness parameters were successfully identified for a multiple-degree-of-freedom (MDOF) nonlinear reduced order model. The nonlinear coefficients identified from the analytical scenario compare well with previously published studies of the beam. Nonlinear parameters were also successfully identified from the raw experimental data. Finally, a MDOF nonlinear reduced order model, constructed from experimental data, was used to predict the experimental response of the beam to other loading conditions. Beam response spectra and average displacement values from the prediction model also compare well with the experimental results.

Modeling and identification of mechanical systems constitute an essential stage in practical control design and applications. Controllers commanding systems that operate at varying conditions or require high precision operation raise the need for a nonlinear approach in modeling and identification. Most mechanical systems used in industry are composed of masses moving under the action of position and velocity dependent forces. These forces exhibit nonlinear behavior in certain regions of operation. For a multi-mass rotational system, the nonlinearities, like Coulomb friction and dead zone, significantly influence the system operation when the rotation changes direction. The paper presents nonlinear modeling and identification of a DC motor rotating in two directions together with real time experiments. Linear and nonlinear models for the system are obtained for identification purposes, and the major nonlinearities in the system, such as Coulomb friction and dead zone, are investigated and integrated in the nonlinear model. The Hammerstein nonlinear system approach is used for identification of the nonlinear system model. Online identification of the linear and nonlinear system models is performed using the recursive least squares method. Results of the real time experiments are graphically and numerically presented, and the advantages of the nonlinear identification approach are revealed.

This paper addresses the issue of automatic identification of backlash in robot transmissions. Traditionally, the backlash is measured manually either by the transmission manufacturer or the robot manufacturer. Before the robot can be delivered to the end-customer, the backlash must be within specified tolerances. For robots with motor measurements only, backlash is an example of an uncontrollable behaviour which directly affects the absolute accuracy of the robot's tool-centrepoint. Even if we do not attempt to bring backlash under real-time control in this paper, we will describe a method to automatically identify/estimate the backlash in the robot transmissions from torque and position measurements. Hence, only the transmissions that do not meet the backlash requirements in the automatic tests need to be checked and adjusted manually.

Simplified models can be useful for up-front design of automotive structures for passenger safety dur-ing crash. Formulations based on the system identifica-tion approach are presented for development of simplified models for simulation and design for automotive crash ...

B-spline neural network (BSNN), a type of basis function neural network, is trained by gradient-based methods that may fall into local minima during the learning procedure. When using feed-forward BSNNs, the quality of approximation depends on the control points (knots) placement of spline functions. This paper describes the application of an artificial immune network inspired optimization method − the opt-aiNet − to provide a stochastic search to adjust the control points of a BSNN. The numerical results presented here indicate that a artificial immune network optimization methods useful for building a good BSNN model for the nonlinear identification of an experimental nonlinear balland-tube system.

Block-oriented models have proved to be useful as simple nonlinear models for a vast number of applications. They are described as a cascade of linear dynamic and nonlinear static blocks. They have emerged as an appealing proposal due to their simplicity and the property of being valid over a larger operating region than a LTI model. In the description of these models, several approaches can be found in the literature to perform the identification process. In this sense, an important improvement is to achieve robust identification of block-oriented models to cope with the presence of uncertainty. In this article, we focus at two special and widely used types of uncertain block-oriented models: Hammerstein and Wiener models. They are assumed to be represented by a parametric representation. The approach herein followed allows to describe the uncertainty as a set of parameters which is found through the solution of an optimization problem. The identification algorithms are illustrated through a set of simple examples.

This paper introduces the four-wheel-drive vehicle REMI, a testbed developed by SAGEM for research purposes in mobile robotics and intelligent car systems. The motion control architecture of the robot is presented, with an emphasis on the guidance and piloting modules. The latter relies on neural network techniques, and the principles underlying its design are outlined. A robust neural control scheme using an internal model of the process is developed. Experimental results are presented.

Most engineering structures include nonlinearity to some degree. Depending on the dynamic conditions and level of external forcing, sometimes a linear structure assumption may be justified. However, design requirements of sophisticated structures such as satellites require even the smallest nonlinear behavior to be considered for better performance. Therefore, it is very important to successfully detect, localize and parametrically identify nonlinearity in such cases. In engineering applications, the location of nonlinearity and its type may not be always known in advance. Furthermore, in most of the cases, test data will be incomplete. These handicaps make most of the methods given in the literature difficult to apply to engineering structures. The aim of this study is to improve a previously developed method considering these practical limitations. The approach proposed can be used for detection, localization, characterization and parametric identification of nonlinear elements by using incomplete FRF data. In order to reduce the effort and avoid the limitations in using footprint graphs for identification of nonlinearity, describing function inversion is used. Thus, it is made possible to identify the restoring force of more than one type of nonlinearity which may co-exist at the same location. The verification of the method is demonstrated with case studies.

A glottal model based on physical constraints is proposed. The model describes the vocal fold as a simple oscillator, i.e. a damped mass-spring system. The oscillator is coupled with a nonlinear block, accounting for fold interaction with the airflow. The nonlinear block is modelled as a regressor-based functional with weights to be identified, and a pitch-synchronous identification procedure is outlined. The model is used to analyse voiced sounds from normal and from pathological voices, and the application of the proposed analysis procedure to voice quality assessment is discussed. 

This paper presents an adaptive neuro-fuzzy inference system (ANFIS) for USD/JPY exchange rates forecasting. Previous work often used time series techniques and neural networks (NN). ANFIS can be used to better explain solutions to users than completely black-box models, such as NN. The proposed neurofuzzy rule based system applies some technical and fundamental indexes as input variables. In order to generate membership functions (MFs), we make use of fuzzy clustering of the output space. The neuro-fuzzy model is tested with 28 candidate input variables for both currencies. For the purpose of comparison, Sugeno-Yasukawa model, feedforward multi-layer neural network, and multiple regression are benchmarked. The comparison demonstrates that the presented algorithm shows its superiority in terms of prediction error minimization, robustness and flexibility.

Most engineering structures include nonlinearity to some degree. Depending on the dynamic conditions and level of external forcing, sometimes a linear structure assumption may be justified. However, design requirements of sophisticated structures such as satellites require even the smallest nonlinear behavior to be considered for better performance. Therefore, it is very important to successfully detect, localize and parametrically identify nonlinearity in such cases. In engineering applications, the location of nonlinearity and its type may not be always known in advance. Furthermore, in most of the cases, test data will be incomplete. These handicaps make most of the methods given in the literature difficult to apply to engineering structures. The aim of this study is to improve a previously developed method considering these practical limitations. The approach proposed can be used for detection, localization, characterization and parametric identification of nonlinear elements by using incomplete FRF data. In order to reduce the effort and avoid the limitations in using footprint graphs for identification of nonlinearity, describing function inversion is used. Thus, it is made possible to identify the restoring force of more than one type of nonlinearity which may co-exist at the same location. The verification of the method is demonstrated with case studies.

This paper is a continuing study of the blind approach for the Hammerstein identification in Sun, and . In the framework of a closed-loop sampled-data system, the output is sampled faster than the updating period of the input. The parameters of the linear dynamics are consistently estimated from the information of the output only, after which the unmeasurable inner signal is uniquely reconstructed. The noise effect is explicitly considered in both the parameter and inner signal estimation. The estimation of the system orders and time delay are studied on the basis of two groups of basic equations obtained by polyphase decomposition. The proposed blind approach is validated and illustrated by a simulated numerical example.

Identiÿcation results for the shaft-speed dynamics of an aircraft gas turbine, under normal operation, are presented. As it has been found that the dynamics vary with the operating point, nonlinear models are employed. Two di erent approaches are considered: NARX models, and neural network models, namely multilayer perceptrons, radial basis function networks and B-spline networks. A special attention is given to genetic programming, in a multiobjective fashion, to determine the structure of NARMAX and B-spline models.

The identification of uncertain and nonlinear systems is an important and challenging problem. Fuzzy models, particularly Takagi-Sugeno (TS), have received particular attention in the area of nonlinear identification due to their potentialities to approximate any nonlinear behavior. A method of nonlinear identification based on the TS fuzzy model and optimization procedure is proposed in this paper. Chaotic particle swarm optimization (CPSO) algorithms, based on chaotic Zaslavskii map sequences, combined with efficient Gustafson-Kessel (GK) clustering algorithm are proposed here for the design of the premise part of production rules, while the least-mean-square technique is utilized for the subsequent part of the production rules of the TS fuzzy model. An experimental case study using a nonlinear yo-yo motion control system is analyzed by the proposed algorithms. The numerical results presented here indicate that the traditional particle swarm optimization algorithm and, particularly, the CPSO combined with GK algorithms are effective in building a good TS fuzzy model for nonlinear identification.

Given a complex first principles model of a process, a strategy for model complexity reduction is developed, such that the model obtained is suitable for process control. The system is assumed to have a Volterra representation that can be parametrized in terms of basis functions with fixed poles. The approach taken consists on iteratively using system identification techniques on the complex system model, while at the same time optimizing the inputs used. The results are tested on a copolymerization reactor example.

We propose a new technique for the identification of discrete-time hybrid systems in the Piece-Wise Affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multi-dimensional domain. In order to achieve our goal, we provide an algorithm that exploits the combined use of clustering, linear identification, and pattern recognition techniques. This allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid avoiding gridding procedures. Moreover, the clustering step (used for classifying the datapoints) is performed in a suitably defined feature space which allows also to reconstruct different submodels that share the same coefficients but are defined on different regions. Measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering and the final linear regression procedure.

In this paper we focus on the identification of discretetime hybrid systems in the Piece-Wise Affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multi-dimensional domain. In order to achieve our goal, we propose an algorithm that exploits the combined use of clustering, linear identification, and classification techniques. This allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid.

An important problem in engineering is the identification of nonlinear systems, among them radial basis function neural networks (RBF-NN) using Gaussian activation functions models, which have received particular attention due to their potential to approximate nonlinear behavior. Several design methods have been proposed for choosing the centers and spread of Gaussian functions and training the RBF-NN. The selection of RBF-NN parameters such as centers, spreads, and weights can be understood as a system identification problem. This paper presents a hybrid training approach based on clustering methods (k-means and c-means) to tune the centers of Gaussian functions used in the hidden layer of RBF-NNs. This design also uses particle swarm optimization (PSO) for centers (local clustering search method) and spread tuning, and the Penrose-Moore pseudoinverse for the adjustment of RBF-NN weight outputs. Simulations involving this RBF-NN design to identify Lorenz's chaotic system indicate that the performance of the proposed method is superior to that of the conventional RBF-NN trained for k-means and the Penrose-Moore pseudoinverse for multi-step ahead forecasting.

This paper introduces the four-wheel-drive vehicle REMI, a testbed developed by SAGEM for research purposes in mobile robotics and intelligent car systems. The motion control architecture of the robot is presented, with an emphasis on the guidance and piloting modules. The latter relies on neural network techniques, and the principles underlying its design are outlined. A robust neural control scheme using an internal model of the process is developed. Experimental results are presented.

This study considers a functional link neural network (FLNN) structure for identifying nonlinear dynamic systems. We tackle the problem of system identification in noisy environments by introducing an adaptive tuning structure based on individual particle optimization (IPO) for the nonlinear systems identification via functional link neural network. The IPO algorithm is applied in order to train the FLNN and achieve the optimum weights of the network for efficiently identifying the nonlinear systems. The proposed optimized FLNN is tested through several experiments, including real-time identification of some nonlinear dynamic systems. Finally, we develop a comparison between the results with the previous counterpart optimized FLNN based LMS, BP, and some evolutionary (GA, PSO, CLPSO) training algorithms. Simulation results verify that the proposed optimization technique, IPO, outperforms these algorithms in the sense of speedup and performance. The remarkable issue addressed here is introducing the IPO algorithm as a real-time optimal tuning technique, which is applicable in other real-time adaptive structures.

We investigate the problem of finding upper and lower bounds of a real valued function of several variables, on the base of a set of noise corrupted values of the function evaluated at a given set of variables and on some assumptions on function regularity and on noise bounds. Several set membership linear and nonlinear identification problems can be recast into the above problem. Two solutions are proposed. The first one is quite straightforward and leads to the definition of bounds that are the tightest ones but, in high dimensional spaces, computationally expensive. The second solution, relying on approximation properties of neural networks, leads to the evaluation of somewhat more conservative bounds, whose computational complexity is significantly lower than for the optimal bounds. A numerical example, related to the identification and prediction of a Lorenz chaotic system is presented to show the effectiveness of the proposed approach

A nonlinear adaptive state-feedback input-output linearizing control is designed for a fifth order model of an induction motor which includes both electrical and mechanical dynamics under the assumptions of linear magnetic circuits. The control algorithm contains a nonlinear identification scheme which asymptotically tracks the true values of the load torque and rotor resistance, which are assumed to be constant but unknown. Once those parameters are identified, the two control goals of regulating rotor speed and rotor flux amplitude are decoupled. Full state measurements are required.

This paper considers certain practical aspects of the identi®cation of nonlinear empirical models for chemical process dynamics. The primary focus is the identi®cation of second-order Volterra models using input sequences that oer the following three advantages: (1) they are``plant friendly;'' (2) they simplify the required computations; (3) they can emphasize certain model parameters over others. To provide a quantitative basis for discussing the ®rst of these advantages, this paper de®nes a friendliness index f that relates to the number of changes that occur in the sequence. For convenience, this paper also considers an additional nonlinear model structure: the Volterra±Laguerre model. To illustrate the practical utility of the input sequences considered here, secondorder Volterra and Volterra±Laguerre models are developed that approximate the dynamics of a ®rst-principles model of methyl methacrylate polymerization. #

This paper describes a simple and cheap solution specifically designed for monitoring the degradation of thin coatings employed for metal protection. The proposed solution employs a commercial photocamera and a frequency domain based approach, that is capable of highlighting the surface uniformity changes due to the initial corrosion. Even thought the proposed solution is specifically designed to monitor the long-time performance of protective coatings employed for restoration of silver artifacts, it can be successfully used also for assessing the conservation state of other ancient metallic works of art. The proposed solution is made tolerant to exposure changes by using a procedure for sensor non-linearity identification and correction, does not require a precise lighting control and employs only free, open source software; so that its overall cost is very low, and can be used also by not specifically trained operators.

Estimation of the modal parameters of mechanical systems or structures is usually achieved by applying the well-known Frequency Response Function (FRF) method to experimental data obtained from free vibration after a shock excitation of the system or forced vibration using a variety of excitation signals. This method is however limited only to linear systems. The problem becomes more complex when nonlinear systems have to be identified. If the nonlinear system is 'well-behaved', i.e. if it shows periodic response to a periodic excitation, 'skeleton' identification using Hilbert Transform techniques may be used to estimate the modal parameters, in function of the amplitude and frequency of excitation. However, Hilbert transform has some limitations. This technique introduces more errors when high damping is present in the system. An improvement is offered by introducing Wavelet analysis to replace the Hilbert transform. This paper deals with the application of the...